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C2×C53×D13⋊C9 #37613601

order24804
automorphism?
homologyAbelianization (H1) = C22×C9×C53 · Schur multiplier (H2) = C2

Aliases

direct productC2×C53×D13⋊C9
unambiguous semidirect productD13⋊(C2×C9×C53)
unambiguous semidirect product(C2×D13)⋊(C9×C53)
unambiguous semidirect product(C13⋊C9)⋊(C22×C53)
unambiguous semidirect product(C2×C13⋊C9)⋊(C2×C53)
unambiguous semidirect product(C2×D13×C53)⋊C9

Splittings

derived, SylowC13 ⋊ C22×C9×C53
HallC53×C13⋊C9 ⋊ C22
HallC2×D13×C53 ⋊ C9
HallC13×C53 ⋊ C22×C9
HallC13⋊C9 ⋊ C22×C53
HallC2×D13 ⋊ C9×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C53D13⋊C3
commutator, hypocenterC13C22×C9×C53
FrattiniC3C2×C53×D13⋊C3
Fitting, socleC2×C3×C13×C53C2×C3
prime radicalC2×C3×D13×C53C3
cosocleC3×C13C22×C3×C53
LCSG ▷ C13
UCSC1 ◁ C2×C3×C53

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12402

Conjugacy classes & character table

2544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 33);